What is the Greatest Common Factor of 1644 and 1664?

Greatest common factor (GCF) of 1644 and 1664 is 4.

GCF(1644,1664) = 4

We will now calculate the prime factors of 1644 and 1664, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1644 and 1664.

How to find the GCF of 1644 and 1664?

We will first find the prime factorization of 1644 and 1664. After we will calculate the factors of 1644 and 1664 and find the biggest common factor number .

Step-1: Prime Factorization of 1644

Prime factors of 1644 are 2, 3, 137. Prime factorization of 1644 in exponential form is:

1644 = 2² × 3¹ × 137¹

Step-2: Prime Factorization of 1664

Prime factors of 1664 are 2, 13. Prime factorization of 1664 in exponential form is:

1664 = 2⁷ × 13¹

Step-3: Factors of 1644

List of positive integer factors of 1644 that divides 1644 without a remainder.

1, 2, 3, 4, 6, 12, 137, 274, 411, 548, 822

Step-4: Factors of 1664

List of positive integer factors of 1664 that divides 1644 without a remainder.

1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 128, 208, 416, 832

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1644 and 1664. The biggest common factor number is the GCF number.
So the greatest common factor 1644 and 1664 is 4.

Also check out the Least Common Multiple of 1644 and 1664